Fallen Seraph said:How random are the digits of irrational numbers? Can it be said of them (i.e. pi=3.14159...) that given any arbitrarily long string of digits it must occur at some point in any irrational number? And would anyone know of anywhere I could find out more on this topic?
Studying the randomness of digits of irrational numbers is important because it helps us understand the nature of these numbers and their distribution. This can have real-world applications in fields such as cryptography and statistics.
To determine the randomness of digits in an irrational number, we can use statistical tests such as the Chi-square test or the Kolmogorov-Smirnov test. These tests compare the distribution of digits in the number to what would be expected in a truly random sequence.
No, there are no known patterns or sequences in the digits of irrational numbers. In fact, one of the defining characteristics of irrational numbers is that their digits are random and non-repeating.
No, we cannot predict the next digit in an irrational number based on the previous digits. Each digit in an irrational number is independent and has an equal probability of occurring.
The randomness of digits in irrational numbers is closely related to the concept of infinity. Since irrational numbers have an infinite number of digits and no repeating pattern, they demonstrate the infinite nature of numbers and the impossibility of fully comprehending them.